After the Commons voted in the affirmative for article 50, Davis urged the Lords to do the same
David Davis stressed that the Government saw off a series of attempts to amend the European Union (Notification of Withdrawal) Bill before it passed through the House of Commons in a "historic" vote by MPs on Wednesday.
The Bill will now need to be approved by peers before Theresa May can begin exit talks under Article 50 of the EU treaties, which she has promised by April.
A government source has stressed the Lords will face an "overwhelming public call to be abolished" if it attempts to frustrate the progress of the legislation.
And Mr Davis told unelected peers not to try to change the simple two-clause Bill as it was passed by MPs unamended, which he said "reflected the will of the people".
I never thought I'd see the day where the House of Commons overwhelmingly voted for Britain to leave the European Union
Asked if the Lords would face "dire recriminations" if it amended the Bill, he told Sky News: "I've seen these bloodcurdling things, they're silly.
"I mean, the simple thing is the Lords is a very important institution.
"I expect it to do its job and to do its patriotic duty and actually give us the right to go on and negotiate that new relationship (with the EU)."
The Liberal Democrats have vowed to continue trying to amend the legislation after it comes to the Lords on February 20 to ensure a second referendum on the final exit deal achieved by Mrs May.
Pro-Europe Tory and Labour peers may also try and make changes to the 'Brexit' Bill.
After 40 hours of debate over five days, Jeremy Corbyn's decision to order his MPs to back the legislation ensured a smooth passage in its final Commons stage, where it was passed by 494 votes to 122 – a majority of 372.
But the Labour leader's authority was called into question after senior frontbencher and ally Clive Lewis quit the shadow cabinet to defy a three-line whip and vote against the Bill.
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The commons yesterday voted with a majority of 372 to allow the government to trigger article 50
As MPs passed through the division lobbies for what many saw as a momentous vote, anti-Brexit Scottish National Party MPs whistled and sang the official EU anthem Ode To Joy, before being told off by Deputy Speaker Lindsay Hoyle.
Another MP was heard to shout "shame" while some Tory MPs applauded the result of the vote, which the Government had tried to avoid before the Supreme Court ruled that Parliament must have a say.
The legislation passed through the Commons without being changed after the Government saw off a series of opposition amendments designed to safeguard against a "hard Brexit".
Ministers also avoided a significant Tory rebellion over the rights of EU citizens already in the UK.
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Continued cooperation with the EU to tackle terrorism and international crime.
Just three Tory backbenchers – Ken Clarke, Tania Mathias and Andrew Tyrie – rebelled to back a bid to make ministers unilaterally guarantee EU nationals' rights.
Other pro-Remain Tories appear to have backed down after Home Secretary Amber Rudd sent them a letter offering them assurances over the issue.
The Government has said it will treat EU nationals' status as a priority in Brexit negotiations and seek to strike a reciprocal agreement to also protect the rights of British expats in Europe as soon as possible.
Parliament voted against an amendment that would guarantee EU nationals' rights in the UK
Brexit-backers such as Boris Johnson and Michael Gove were ridiculed after voting against an amendment calling on the Government to keep the Leave campaign's promise that quitting the EU would allow £350 million extra to be spent on the NHS every week.
Labour MP Chuka Umunna said Tory MPs who campaigned to leave and opposed the amendment should "hang their heads in shame".
A total of 52 Labour MPs, including 11 frontbenchers and three whips, rebelled against Mr Corbyn's orders and voted against triggering Article 50.
52 Labour MPs rebelled against the party whip and voted against triggering article 50
Former chancellor Mr Clarke was again the only Conservative to vote against the Bill.
Former Ukip leader Nigel Farage, a leading Brexit supporter, said: "I never thought I'd see the day where the House of Commons overwhelmingly voted for Britain to leave the European Union."
Mrs May's immediate attention will now turn to a meeting at Downing Street with Italian prime minister Paolo Gentiloni on Thursday, in which the pair are sure to discuss Brexit.